package com.jxb.dp20251355;

import java.util.Arrays;

/**
 * 类注释
 *
 * @author jiaobo
 * @date Created in 2025/1/6 21:38
 **/
public class UniquePaths_62 {

    //状态转移公式：dp[i][j] = dp[i-1][j] + dp[i][j-1]
    public int uniquePaths(int m, int n) {
        //定义状态转移公式
        int[][] dp = new int[m][n];
        //进行初始化
        for (int i = 0;i<m;++i) {
            dp[i][0] = 1;
        }
        for (int j = 0;j<n;++j) {
            dp[0][j] = 1;
        }

        //填充dp数组
        for (int i = 1;i<m;++i) {
            for (int j = 1;j<n;++j) {
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        }
        return dp[m-1][n-1];
    }

    //状态转移公式：dp[j] = dp[j] + dp[j-1]
    public int uniquePaths2(int m, int n) {
        int[] dp = new int[n];
        //初始化
        Arrays.fill(dp,1);
        //循环遍历，执行状态转移公式
        for (int i = 1;i<m;++i) {
            for (int j = 1;j<n;++j) {
                dp[j] = dp[j] + dp[j-1];
            }
        }
        return dp[n-1];
    }

}
